Abstract In this research work, a newly-proposed multiterm hybrid multi-order fractional boundary value problem is studied. The existence results for the supposed differential equation that involves Riemann–Liouville derivatives and integrals of multi-orders type are derived using Dhage’s technique, which deals with composition three operators. After that, its stability analysis Ulam–Hyers rele...

In 1940 and 1964, Ulam proposed the general problem: “When is it true that by changing a little the hypotheses of a theorem one can still assert that the thesis of the theorem remains true or approximately true?”. In 1941, Hyers solved this stability problem for linear mappings. According to Gruber 1978 this kind of stability problems are of the particular interest in probability theory and in ...

In this paper, we investigate the generalized Hyers-Ulam stability of a bi-reciiprocal functional equation in quasi-β-normed spaces. AMS Mathematics Subject Classification (2010): 39B82, 39B72

In this paper, we obtain the Hyers–Ulam–Rassias stability of the generalized Pexider functional equation ∑ k∈K f(x+ k · y) = |K|g(x) + |K|h(y), x, y ∈ G, where G is an abelian group, K is a finite abelian subgroup of the group of automorphism of G. The concept of Hyers–Ulam–Rassias stability originated from Th.M. Rassias’ Stability Theorem that appeared in his paper: On the stability of the lin...

We construct  a noncommutative analog of additive functional equations on discrete quantum semigroups and show that this noncommutative functional equation has Hyers-Ulam stability on amenable discrete quantum semigroups. The discrete quantum semigroups that we consider in this paper are in the sense of van Daele, and the amenability is in the sense of Bèdos-Murphy-Tuset. Our main result genera...

We will apply a fixed point method for proving the Hyers–Ulam stability of the functional equation f(x+ y) = f(x)f(y) f(x)+f(y) .

We study the generalized Hyers-Ulam stability of the functional equation f[x1,x2,x3]= h(x1+x2+x3). 2000 Mathematics Subject Classification. 39B22, 39B82.

In 1940, Ulam proposed the stability problem see 1 : Let G1 be a group and let G2 be a metric group with the metric d ·, · . Given ε > 0, does there exist a δ > 0 such that if a mapping h : G1 → G2 satisfies the inequality d h xy , h x h y < δ for all x, y ∈ G1 then there is a homomorphism H : G1 → G2 with d h x ,H x < ε for all x ∈ G1? In 1941, this problem was solved by Hyers 2 in the case of...

In this paper, we study Hyers–Ulam and generalized Hyers–Ulam–Rassias stability of a system hyperbolic partial differential equations using Gronwall’s lemma Perov’s theorem.

In this paper, we investigate the exact and approximate controllability, finite time stability, β–Hyers–Ulam–Rassias stability of a fractional order neutral impulsive differential system. The controllability criteria is incorporated with help fixed point approach. famous generalized Grönwall inequality used to study stability. Finally, main results are verified an example.